Ibrahimovic settled the match with a delightful chip in the 49th minute, having notched his first league goal for Milan since his move from Barcelona in Wednesday’s 1-1 draw at Lazio.
Victory gives Milan eight points from five games, two points fewer than leaders Inter Milan, who lost 0-1 away to struggling Roma later on Saturday.
“This win counts for a lot because it’s important to be in good shape psychologically,” Milan coach Massimiliano Allegri told Sky television.
“When the results don’t come, you always worry, even if you’re a great team.”
Robinho was in Milan’s starting line-up for the first time since arriving from Manchester City and he and fellow forwards Ibrahimovic and Ronaldinho tried to make things happen by switching positions early on.
The visitors closed them down well though and the first episode of note was a powerful shot by Genoa’s Rafinha that flew just past the post in the 14th.
Robinho had an angled shot well saved by Eduardo soon after and the Portugal goalkeeper also denied Gennaro Gattuso from close range as Genoa frustrated Milan by being miserly with space.
The hosts almost went behind in the 39th when keeper Christian Abbiati diverted a Rodrigo Palacio cross onto his own far post before a largely uneventful first half came to an exciting close.
Ghana midfielder Kevin-Prince Boateng, who was loaned to Milan by Genoa straight after signing from Portsmouth in the close season, pounced on a defensive lapse but Eduardo was on hand again to repel his effort.
Abbiati then produced a stunning save at the other end to keep out a bullet header by Spanish defender Chico.
The deadlock was shattered soon after the break when Ibrahimovic resisted the attention of two markers to get his toe to Andrea Pirlo’s pass from deep, with Eduardo unable to save despite getting finger-tips to the looping ball.
Milan sat on their lead in comfort. Ronaldinho almost made it 2-0 on the hour with a strike that sailed just over the bar and Robinho had a shot cleared by Domenico Criscito with Eduardo beaten, while Mathieu Flamini squandered two good opportunities in the closing stages.
This weekend’s Serie A action is taking place after Italian professional footballers union AIC postponed a strike called over a contract wrangle.
Juventus, who have so far shown few signs of improving on last season’s miserable campaign despite an array of signings and the arrival of new coach Luigi Delneri, take on Cagliari at home when the rest of the programme is disputed on Sunday.